Units
(: title International System of Units (SI) :)
Base Units
The History of meter and second.
At the moment, 1 second is defined of 9,192, 631,770 cycles of the standard Cs-133 transition (!!!) and 1 meter is defined as a distance travelled by light in vacuum in 1/299,792,458 s (!!!!!). and c = 299,792,458 m/c is accepted as a constant.
But historically we actually had to measure the speed of light first (and we did not even know it is constant) and had no way to get such a short stable period of time to count cycles. Thus how survived until 2015?
1) Time. The only "stable" oscillator available for humans from the beginning of the world is earth rotation. Thus solar clock were invented - a shadow from pole does make a full run over the 360 deg through the day+night, and we can divide it accurately into fractional parts of our choice - and call 1/24 an hour and 1/3600 a second.
2) Distance. Even easier with length, we can take *a* stick of a size compatible with our body dimensions and agree to measure everything related to this etalon. Thus we used feet, yards, "arshin", "locot'" e.t.c.
3) Speed of light. We did not have to care until we realized that it is a universal constant .... later. and connect distance and time as $\lambda \times \nu = c$ when we played with electromagnetic waves. So one can measure "\lambda", the wavelength of some light with an "interferometer" in "old" meters, and number of transitions between energy levels of electrons in some atom during "old" seconds; and find the speed of light. Now we know that c is a constant - and we fix it near the number we get. We also can fix a number of cycles in our "second", and then define length the way we used it now.
Derived Units
Other Systems (HS+)
Dimensional Analysis
Covert liters per 100 km to miles per gallon.